Sometimes we make the same mistakes over and over again when we deal with problems because we lack in certain areas. By strengthening the connection between different types of problem solving methods – patterns – we learn to deal with problems through different perspectives.

Below are 77 problems that will enable you to strengthen that connection by finding out what kinds of problems you already are good at and which ones you might need to work on.

These categories -while being different in some aspects also- interconnect in many ways. Many involve the process of first finding the pattern of the problem and from there work on a solution. They all follow logical thinking in one way or the other. The more you improve on each category the stronger will their connection become and your overall creativity will improve as a result.

The problems that you cannot work out immediately are the ones that should be seen as opportunities that develop your creativity. When a problem is difficult, you will evolve your creative thinking by working on solving it and figuring out solutions that are logical.

Math & Probability Problems

Neither one of us will get through life very easily without basic mathematical understanding. People who have developed their mathematical intelligence generally have the ability to reason and calculate essential calculations, as well as using and manipulating equations. With basic mathematical intelligence you don’t need to be very flexible (as you often need to be when dealing with logical problems which are presented below), so to spice things up a bit, I’ve also placed a few probability problems that might further challenge your mathematical reasoning.

1. Age

Gerald who is twelve years old is three times as old as his sister Jane.How old will Gerald be when he is twice as old as Jane?

13 years - 16 years - 17 years - 19 years - 22 years

2. Sequence Problem

In this sequence below, each term after the first is determined by multiplying the previous term by x and then adding y. What number is n?

4, 13, 40, 121, n

3. Replace X

Which number should replace X?

a) 3
b) 5
c) 9
d) 18

4. Simplify Expression

Simplify the expression below.
2(a -3) + 4b - 2(a -b -3) + 5

5. Bakers' Cookies

If it takes 5 bakers, 250 minutes to make 500 cookies. How many minutes would it take for 2 bakers to make the same amount of cookies?

6. Middle Number

Same functions are applied to reach the results in each of the sets of numbers. What number should replace X?

7. Fill in the Sequence

Fill in the sequence, what is X?

9, 12, 18, X, 43

8. Majoring Students

At a University, all of the students are majoring in statistics or business, or both. 55 % of the students are statistics majors and 77 % are business majors. If there are a total of 500 students, how many of them are majoring in both statistics & business?

9. Random Employee

At A-MadeUp Corporation, there are 632 men and 593 women. One employee will randomly be chosen to receive a bonus. What percent chance is there that it will be a woman? Round to the nearest whole percent.

10. Possible Outcomes

A diagram used to show the total number of possible outcomes in a probability experiment is called what?

11. Classic: Monty Hall Problem

Here's a classic probability problem, called the Monty Hall Problem.

Imagine you're in a game show called Let's make a deal, where you are presented with three closed doors. Behind two are goats, and behind one of them is the actual prize, a car. Now, you begin the game by choosing one door. Once you have done that the host walks up and opens one of the two other doors and presents one of the goats. He then asks you if you want to stay at your chosen door or if you want to switch?What choice of action would give you the highest probability of choosing the door with the car?

12. Another Number Sequence

What is n?

1, 3, 15, 255, n

* You might need a calculator.

13. How Old is Elin?

Amy is twice as old as Elin. In four years the sum of Amy and Elin will be 20. How old is Elin?

14. Placement of Cards

Three playing cards, taken from a normal pack, are placed face down on a table in a row. To the right of a king there are one or two queens. To the left of a queen there are one or two queens. To the left of a heart there are one or two spades. To the right of a spade there are one or two spades.

20. Logical Sequence

Verbal Intelligence Problems

If you are strong in verbal intelligence then typically that makes you good at memorizing information and using words well both when writing and speaking. With verbal intelligence one usually is referring to the ability to evaluate information and solve problems using reasoning that is based on language.

21. Rearrange and Categorize

Rearrange the following letters to make a word and choose the category in which it fits.

"AIGNAHSH"

a) City
b) Ocean
c) Vegetable
d) Flower

22. Which Word?

Which one of the sets of letters below can be arranged into a six letter English word.

a) OMLAGA
b) ATRUNE
c) FASUPA
d) NINEGE

23. Find the Answer

Find the answer that best completes the analogy.
Nonsensical:Ridiculous :: Indignant : ?

a) Supercilious
b) Ironic
c) Infuriated
d) Rash

24. Matching

Match the column A and B by identifying one pair, one word from each group, that is closest in meaning.

25. Association

Murrey is to Black as Magenta is to

...green
...blue
...red
...white

26. Remove 6 Letters

If you remove 6 letters from the word SIGNIFICANCE, can the word FIANCE be formed?

27. Finding E

The third consonant appearing at the beginning of this sentence is the letter "e."?

28. Makes Sense?

Does the following sentence makes sense if you write "golas" instead of "paint":

Jack loves to golas, in fact he golashed all night long.

29. English Alphabet

In the English alphabet, how many letters are there between the letter F and the letter T?

30. Words found in Words

Can the word ENTIRE be spelled using only the letters found in the word RETIREMENT?

31. Synonym

If a person is choleric, that means they are:

a) obese
b) happy
c) peevish
d) athletic

32. Association

Begin is to End as Born is to

...birth
...die
...enough
...complete

33. Missing Letter

Find what the missing letter is.

34. Alphabetical order

If the words in the following questions were arranged in alphabetical order, then which word would come third.
Jargon - Jaguar - Jacuzzi - Jail - Jazz

35. Word Grid

Find four words, horizontally, vertically or diagonally.

36. Find the Letter

What letter should replace the question mark?

Logical Intelligence Problems

Sometimes logical intelligence is said to be the same as mathematical intelligence. Here we will make a distinction; the problems listed below are more conceptual than the mathematical ones you dealt with above. With strong logical reasoning you are good at estimating solutions, analyzing problems and thinking abstractly about numbers.

37. The Ball

How can you throw a ball and have it come back to you, even if it doesn't bounce off anything? There is nothing attached to it, and no one else catches or throws it back to you.

38. Make a Square

Make a square by only moving one of the matches.

39. Months

Each month have different amounts of days. How many months have 28 days?

40. What Day is It?

The day after the day after tomorrow is four days before Tuesday. What day is it today?
Monday
Tuesday
Wednesday
Thursday
Friday

41. Is to

Forest is to tree as tree is to:
plant
leaf
branch
yard

42. Triangle Logic

What should X be, if it follows the same formula as the other two triangles?

43. Classic: Hand Shakes

At a meeting, 14 members shook hands with each other before & after the meeting.How many total number of hand shakes occurred?

44. Mathematical Symbol

Put a mathematical symbol between 6 & 9 to get a number which is greater than 6 but lesser than 9.

45. Prove it

Prove that removing 1 from 19 makes 20.

46. 615182021145

518119518 is to Eraser as 615182021145 is to...

Interest
Fortune
Money
Abandon

47. Shortest

Alan is taller than James and Andy. James is taller than Miranda. James and Miranda are taller than Emma. Miranda is shorter than Andy. Who is the shortest?

48. Visual Logic

Remove 7 matches to get nine.

Pattern Recognition Problems

You’ve now had some practice with pattern recognition if you’ve worked with the problems above. It’s time for some pure pattern recognition problems. How good are you at finding similarities in different symbols, words and images? Pattern recognition is the ability to make out presented or rising patterns. It is a vital skill if you want to get good at predicting what will happen next in situations.

54. Favorite Numbers

55. Letter Design

56. Flower Patterns

From Mensa.orgWhich of the figures below the line of drawings best completes the series?

57. Word Play

If the word REASON can be coded as TGCUQP, then how can you code the word IMPACT?

+ TCAPMI
+ QVVSON
+ TCGPQU
+ KORCEV
+ EIPACT

58. Letters in Sequence

Which of the following letters does not belong in the sequence?
A, E, I, F, U

59. 24 H in a D

24 H in a D is "short for": 24 hours in a daySolve the ones below:

a) 12 M in a Y
b) 7 W of the W
c) 64 S on a C B
d) 26 L of the A

60. Dots

Which option should come next?

61. Dots 2

Which option below should come next?

Lateral Thinking Problems

Lateral thinking problems are problems that often need to be thought of twice before solved. They are not typical logical problems but are designed to force you to think in different terms than you usually do. Below are some classical lateral thinking problems, some more common than others.

62. Classic: Didn't Drown

A man who couldn't swim fell off a yacht into deep water. He was not wearing anything to keep him afloat. It took 30 minutes for the people on the yacht to realize someone was missing, and the man was rescued two hours later. Why didn't he drown?

63. Classic: What am I?

My life can be measured in hours,
I serve by being devoured.
Thin, I am quick
Fat, I am slow
Wind is my foe.What am I?

64. Right Hand

What can you hold in your left hand but never in your right hand?

65. Classic: Six Eggs

Six eggs are in a basket. If six individuals each take one of the eggs, then how come one of the eggs is still left in the basket?

66. Who is Behind Who?

Amy is standing behind Tina, and Tina is standing behind Amy. How is this possible?

67. Classic: Condemned

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven't eaten in 3 years. Which room is safest for him?

68. Classic: Three Switches and Three Bulbs

Three switches outside a windowless room are connected to three light bulbs inside the room. How can you determine which switch is connected to which bulb if you may enter the room only once?

Visual Spatial Intelligence Problems

People with strong visual spatial intelligence are often described as artistic as they are very conscious of their surroundings and good at remembering visuals. If you have a strong visual spatial ability then it's very likely that you enjoy drawing. You will also have a strong sense of orientation and take pleasure in reading maps and blueprints.

The answer provided for the rubic cube problem (A) is incorrect. In fact, the choice A is not even a valid cube as there are 10 red squares shown while the cube only has 9 of each color. The actual correct answer should be C.